#1042 ⟨a, b, c | ab=c, bcc=a⟩

Properties

Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element a has infinite order
Submonoid of enveloping group: ⟨a, b | aaabb⟩
- Embedding: φ(a) = ab^-1a^-1, φ(b) = ab, φ(c) = a

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Reduction order:
- Left-to-right recursive path with deg(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=c,bcc=a ab/c - -
baa=aab
babab=a
c=ab

12 unique, 171 total

Σ	#	Presentation	Properties	φ
7	279	⟨a, b, c \| aaa=b, cbc=1⟩	Grp Inf	146
7	543	⟨a, b, c \| ba=ac, cb=a⟩	Can Inf
7	555	⟨a, b, c \| bb=ac, cb=a⟩	Can Inf	4
7	558	⟨a, b, c \| bb=ac, cc=a⟩	Can Inf	2
7	937	⟨a, b, c \| aa=b, cbc=a⟩	Can Inf	2
8	3045	⟨a, b, c \| aba=c, abc=b⟩	Can Inf	2
8	3051	⟨a, b, c \| aba=c, bab=c⟩	Can Inf
8	3071	⟨a, b, c \| abc=b, bca=c⟩	Can Inf	2
8	3595	⟨a, b, c \| ba=ac, cb=ac⟩	Can Inf
8	5663	⟨a, b, c \| aa=b, aaa=cc⟩	Can Inf	1
8	6019	⟨a, b, c \| ab=c, aba=bc⟩	Can Inf
8	6071	⟨a, b, c \| ab=c, bac=ca⟩	Can Inf

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ	#	Presentation	Mapping
8	3055	⟨a, b, c \| aba=c, bcb=a⟩	φ(a) = a, φ(b) = b, φ(c) = aba
8	5562	⟨a, b, c \| ab=c, babc=a⟩	φ(a) = a, φ(b) = b, φ(c) = ab